connecting the graph of the sine function to the unit circle. procedure: at each arrow, - get the terminal…

connecting the graph of the sine function to the unit circle. procedure: at each arrow, - get the terminal point on the unit circle. - identify the coordinates of its ordered pair as the sine function. corresponding to t = π/2, the coordinates of the terminal point are (x,y)=(0,1). the value of the sin(t) function is 1 (answer should be a number). question 2 2 pts the next arrow case for which the terminal point has the same coordinates with the terminal point for a2 is (select one): a4 b1 b4 b2 b3 a3
Answer
Answer:
For the first - part:
0, 1, 1
For the second - part:
A4
Explanation:
Step1: Recall unit - circle properties
For $t=\frac{\pi}{2}$, on the unit - circle, the terminal point coordinates are $(x,y)=(0,1)$.
Step2: Recall sine function definition
The sine function is defined as $\sin(t)=y$. For the point $(0,1)$ on the unit - circle, $\sin(\frac{\pi}{2}) = 1$.
Step3: Analyze periodicity of the sine function
The sine function $y = \sin(t)$ has a period of $2\pi$. If we consider the points on the unit - circle and their corresponding sine - wave graph, the pattern repeats every $2\pi$. If we assume that the points on the graph follow the periodic nature of the sine function, and we know that the sine function has a period such that the values repeat. If we consider the symmetry and periodicity of the sine function and the unit - circle relationship, the point that will have the same coordinates as a given point on the unit - circle (and thus the same value of the sine function) will be separated by a full period. In the context of the given points on the graph, the point that has the same coordinates as A2 is A4.